Cone Definition and 490 Threads

Homework Statement A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder. I'm just really confused on how to figure this one out. The equation for the volume of a cone is v = 1/3pi r^2h and the volume of a...

1. Find the electric field at the tip of a cone of height and radius R with uniform surface charge density \sigma . I get that the field diverges at the tip, which is puzzling because it's not as though there's a point charge at the tip. I thought this sort of thing can't happen when you...

Homework Statement Given Parameterization: x = u cos \phi y = sin \phi z = u cot \Omega Find the sloping surface of a right cone with semi-angle \Omega with a base radius of a. Homework Equations Surface area of a cone = \pi r\sqrt{r^2 + h^2} The Attempt at a Solution...

I am looking to test detect if a cone (described by an apex, angle theta and axis) and a sphere (defined by a sphere centre and a radius) intersect. Please see here for a complete description (because i can't post the code here)...

Perhaps someone with a lot of patience would help me. I am watching Roger Penrose Clocks at the Big Bang 09/30/2008 on PIRSA http://streamer.perimeterinstitute.ca/mediasite/viewer/NoPopupRedirector.aspx?peid=940fba57-4cf9-4659-9c2d-1324d45cf4e4&shouldResize=False# At about 37 minutes...

Homework Statement Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo) Homework Equations I know I need to somehow use the equation I= intergral r^2 dm...

Homework Statement Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. (see attached photo) Homework Equations I know I need to somehow use the equation I=\intr2dm also, I...

I posted a similar question under cosmology but the question was unable to be answered. I thought I would try a reframe the question. When approaching a black holes event horizon, the exit cone for light become smaller until it is eliminated at the event horizon itself. But how can gravity...

Homework Statement Triple integral of 1+z inside the cone z=2sqrt(x^2+y^2) above the xy plane and bounded by z=6 Homework Equations The Attempt at a Solution when z=6, 6=2sqrt(r^2) so r=3 limits of integration are z=6 to z=2r r=3 to r=-3 theta=2pi to theta=0 Just want to make...

Homework Statement So there's about 4 problems that iI just don't understand. The first one is called H20 in the S-K-Y. Theres a drawing and it kind of looks like a graduated cylinder with a circle on top. It says the spherical top holds a little over 54,000 gallons of water, the base of...

Homework Statement The question is to derive the surface area of a cone. Homework Equations slant= square root ( r^2 + h^2) surface area= int int [square root(fx^2 + fy^2 +1) da] surface area of cone side= pi *r(r^2+h^2) 3d cone formula: z= h/r(squareroot x^2+y^2) The Attempt at...

Homework Statement Hi Im having some difficulty with the following question: Figure P1.14 shows a frustrum of a cone. Of the following mensuration (geometrical) expressions, which describes (a) the total circumference of the flat circular faces, (b) the volume, and (c) the area of the...

Please I need a respectable proof how to get the volume of the truncated cone. I need it really quick. So please could you help me. No numbers just "the method" how to get that formula. Thanks.

1. The problem statement The problem requires me to calculate the flux of F=x^2 i + z j + y k out of the closed cone, x=sqrt(y^2 + z^2) with x between 0 and 1. I am having trouble approaching this problem because most of the problems I have done give the curve as z=f(x,y) instead of...

Dear All I have a problem that can be represented in two different forms. Problem is related to propagation of waves in 2D space with respect of time. I have three random points in the 3D Space. How many right circular, infinite cones with specific predetermined angle between conical...

Homework Statement You look directly overhead and see a plane exactly 1.4·km above the ground, flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.4·km. (a) Find the angle of the shock wave cone. (b) Find the...

Homework Statement A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep. Homework Equations Cone: V= (Ah/3) Right...

Lets assume we have a resistor material, with a perfect solid spherical shape and no defect, we connect it from south pole to north pole, by using the general formula of R=(rho)L/A where rho is the resistivity and L is the length of the resistor, and A is the cross sectional area. I found that i...

The question is this: find the centroid of the half-cone sqrt(x^2 + y^2) <(oet) z <(oet) 1 and x >(oet) 0 (oet being or equal to, I apologize for the lack of sophistocated symbols). I thought I was doing it correctly, but my answers do not match up with those in the book. I assumed...

If there is a frustum with base radii of 1.75 and 1.25 inches, and a height of 6 inches, what is the volume? I tried to use the V=|(b1*h1)/3-(b2*h2)/3)| from the Wikipedia page, but h2 is unknown. I get an answer of 42.41 in^3. Is this correct? Please use basic calculus as that is all I have...

1. The slant edge of a right circular cone is 6 cm in length. Find the height of the cone when the volume is a maximum. 2. Find the maximum volume of a right circular cone whose slant edge has a constant length measure a.

Suppose you wanted to make an ice cream cone that would hold as much ice cream as possible (do not assume ice cream comes in spheres). Challenge I Cut a wedge from a circle and remove it. From the remaining piece of the circle into a cone. Find the angle of the wedge that produces the cone...

Homework Statement Find the volume of an ice cream cone bounded by the sphere x^2+y^2+z^2=1 and the cone z=sqrt(x^2+y^2-1) Homework Equations The two simultaneous equations yield x^2+y^2=1 The Attempt at a Solution Attached

Hi, I'm working on a related rates problem, and I need to find the derivative of the volume of a cone. So the equation is: V = (1/3) (pi) (r^2) (h) I'm not sure how to find the derivative. Would the whole thing turn out to be 0? Or do I need to use the product rule? Please help...

Homework Statement The volume of a right circular cone is V = [(pie)(r^2)(h)]/3 and it ssurface area is S = (pie)(r)(r^2+h^2)^(1/2), where r is the base radius and h is the height of the cone. Find the dimensions of the cone with surface area 1 and maximum volume. The Attempt at a Solution...

A 0.25 kg pine cone falls from a branch 20 m above the ground. A) With what speed would it hit the ground if air resistance could be ignored? m= 0.25 kg g= 9.8 m/s^2 d= 20 m Ep= (0.25kg)(9.8m/s^2)(20m) = 49 J Ek= 1/2mv^2 49J = 1/2(0.25kg)(v^2) 2(49 J = (0.5kg)(0.5 v^2)) 98 J =...

Find the mass of a right circular cone of base radius r and height h given that the density varies directly with the distance from the vertex does this mean that density function = K sqrt (x^2 + y^2 + z^2) ? is it a triple integral problem?

Hi all, Homework Statement Given a right circular cone with origin at the centre of the base, the positive z-axis pointing towards the apex, and the height is h and radius of base is r. What is the cartesian equation of the cone? Homework Equations The Attempt at a Solution...

Homework Statement Find the moment of inertia of the right circular cone or radius r and height h with respect to its axis, and in terms of its mass. *As of this point, I am supposed to use solids of revolution, and so I need to rotate a line about an axis, and find the moment of inertia with...

Hi! I have a question and would greatly appreciate your help. I've been wondering about how a light that is a emitted in the shape of a cone from a source (such as, a flashlight) can reach certain points outside the cone of light (although, much less intensly). The simple answer you are...

When discussing EPR experiments on this forum I made the claim that Bell's theorem does not prove classical determinism false because there is always the possibility that the correlations between distant measurements can be a result of the common past shared by particle source and the two...

:confused: PROBLEM: A cone with a 30degree angle and a hieght of 1 must fit a sphere of icecream in it with a maximum volume. what is that volume, and what percentage of the sphere is in that cone!? PLEASE HELP!? this is all i have R= (h-a)(sin15) a=distance between center of sphere...

Homework Statement Consider a cone of height H and base radius R with its apex (tip) at the origin, and its base at circular end at z = H. Derive the equation for the surface of the cone in cylindrical coordinates. You may assume z is proportional to r. Homework Equations I assume the...

Source: Physics and Scientists for Engineers, Ch. 24 #7 A cone of radius R and height h sits on a horizontal table. A uniform electric field parallel to the table penetrates the surface of the cone. What is the flux entering the cone? Diagram: (N.B. the dots in the cone are just to give it...

Homework Statement Water is draining from a conical tank with height 12 feet and diameter 8 feet into a cylindrical tank that has a base with area 400 \pi square feet. The depth, h, in feet, of the water in the conical tank is changing at the rate of (h-12) feet per minute. A) Write an...

Homework Statement Dynamics Problem: Spinning cone with mass!? The sides of a cone make an angle "THETA" with the vertical. A small mass "m" is placed on the inside of the cone and the cone, with its point down, is revolved at a frequency "f" about its symmetry axis. If the coefficient of...

I am wondering if someone can help clarify the following? Suppose that I’m asked to find the volume of a cone. So, the volume would be ∫∫∫dxdydz or using polar coordinates ∫∫∫rdzdrdθ. Therefore the volume would be if I have a cone with base radius R and height H, I can express the radius r at...

Homework Statement find electric flux that enters left hand side of a cone (with base radius R and height h). electric field penetrates the cone horizontally (cone is on a horizontal table). Homework Equations flux = surface integral of EdA where E represents component of electric...

im actually bugged of finding a solution for d topic mentioned can any 1 pleasezzz help me

1. I have a cone frustum with known height (h) and known base diamter (d) and cap diameter (D). From this, I can calculate the volume. Question: if the frustum is half full of liquid, how can I calculate the height of the liquid? 2. V = pi/12 x h x (D2 + d2 + D x d) 3. I guess I...

Hi! Please follow the link; its a guy juggling balls in an inverted cone. What he does is he uses the cone as a surface, and he rolls the balls around him in circles. ITs really entertaining so this shouldn't be too much of a chore. I thought I'd post it here because it demonstrates simple...

Find the location of the CM of a hollow ice cream cone, with base radius R and height h, and uniform mass denisty. How does your answer change if the cone is solid, instead of hollow? Okay, so I'm pretty sure that I need to work with slices, and that you need the mass which I believe is...

Hello there, this is my first posting on this board. I am a third year physics major and I've taken a lot of courses but I've always just scraped by with a large amount of help from small groups. I'm thinking about reconsidering my major because I feel like I no longer can understand the...

I'm stuck on this question: "A man is sipping soda through a straw from a conical cup, 15 cm deep and 8 cm in diameter at the top. When the soda is 10 cm deep, he is drinking at the rate of 20 cm^3/s. How fast is the level of the soda dropping at that time?" So you are given height = 15...

Here's a cute problem I came across recently. Suppose you have a rubber band with spring constant k, mass m and unstretched radius r. Now suppose you have a frictionless cone and the angle of the peak is 2 \theta (that is, if you project the shape of the cone onto a plane it looks like a...

I stumbled across this while looking for something else. This might be of interest to AE's. http://en.wikipedia.org/wiki/Nose_cone_design

Ok i need to calculate the work done by gravity , while filling a truncated cone of bottom radius R and upper radius r (R>r) and height H , with sand of density 'd' , if we start filling the cone from bottom.. What i did was , I considered a disc of radius 'x' as a part of the cone and with...

I have been presented with this problem. I somewhat know what I need, I just don't know how to get it :blushing: The problem: A truncated cone, top diameter of 1m bottom diameter of 1.5m and a height of 10m. With a given density(I do not have it with me at this moment, I do not remember...

sphere in a cone (ball in a martini glass) A problem a friend mentioned to me years ago. You have a cone with height H and angle A. What is the radius R of a sphere that when placed in the cone, displaces the most volume? One suggestion was to reduce this to a two dimensional case.

Surface area integral sorry, this is not about flux integration... but surface area! sorry about the title! Find the surface area of the part of the sphere x^2+y^2+z^2=36 that lies above the cone z=\sqrt{x^2+y^2} z=\sqrt{36-x^2-y^2} A(S)=\int\int_D \sqrt{1+\left( \frac{\partial...